Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 66 inches and standarddeviation 6 inches.
(a) What is the probability that an 18-year-old man selected atrandom is between 65 and 67 inches tall? (Round your answer to fourdecimal places.)
(b) If a random sample of twenty-three 18-year-old men is selected,what is the probability that the mean height x is between65 and 67 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probabilityin part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standarddeviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean issmaller for the xdistribution.
The probability in part (b) is much lower because the standarddeviation is smaller for the x distribution.
The probability in part (b) is much higher because the standarddeviation is larger for the x distribution.
The probability in part (b) is much higher because the mean islarger for the x distribution.
